We discuss our progress towards testing whether humans can see single photons, using a single-photon source based on spontaneous parametric downconversion and techniques from quantum optics. We review the existing evidence on single-photon vision, and show why no previous experiments with classical light sources (or otherwise) have truly been able to test it. We describe the heralded single-photon source we have built, which can be used for a definitive single-photon vision test, and discuss the statistical requirements and challenges of such a test. In pilot studies, we demonstrate that a two-alternative forced-choice design and our observer viewing station can measure the perception of very weak visual stimuli (including the weakest flashes of light ever directly tested, with just ~3 photons absorbed). We present two proposed experiments to test quantum effects through the visual system, which could contribute to our understanding of wavefunction collapse and the quantum-classical transition. We also discuss our work on other questions related to visual perception near threshold, including the length and completeness of temporal summation, which we have investigated in detail with a new experimental paradigm. We found that temporal summation continues for at least 650 ms when photons are delivered at a rate of about 30 in 100 ms, and that the completeness of summation may remain efficient over this window. Finally, we present some preliminary results on how 8- to 13-Hz alpha oscillations in the brain (which have complex effects on neural excitability and visual perception) might impact the detection of few-photon stimuli.